Problem: $\dfrac{ -5g - 4h }{ -3 } = \dfrac{ g - 3i }{ -5 }$ Solve for $g$.
Multiply both sides by the left denominator. $\dfrac{ -5g - 4h }{ -{3} } = \dfrac{ g - 3i }{ -5 }$ $-{3} \cdot \dfrac{ -5g - 4h }{ -{3} } = -{3} \cdot \dfrac{ g - 3i }{ -5 }$ $-5g - 4h = -{3} \cdot \dfrac { g - 3i }{ -5 }$ Multiply both sides by the right denominator. $-5g - 4h = -3 \cdot \dfrac{ g - 3i }{ -{5} }$ $-{5} \cdot \left( -5g - 4h \right) = -{5} \cdot -3 \cdot \dfrac{ g - 3i }{ -{5} }$ $-{5} \cdot \left( -5g - 4h \right) = -3 \cdot \left( g - 3i \right)$ Distribute both sides $-{5} \cdot \left( -5g - 4h \right) = -{3} \cdot \left( g - 3i \right)$ ${25}g + {20}h = -{3}g + {9}i$ Combine $g$ terms on the left. ${25g} + 20h = -{3g} + 9i$ ${28g} + 20h = 9i$ Move the $h$ term to the right. $28g + {20h} = 9i$ $28g = 9i - {20h}$ Isolate $g$ by dividing both sides by its coefficient. ${28}g = 9i - 20h$ $g = \dfrac{ 9i - 20h }{ {28} }$